If `(a)/(8) =(b)/(9) = (c )/(6)`, then `(a+ b + c)/(c )` is equal to _________.

Options

A. 7
B. `2(1)/(2)`
C. `3(5)/(6)`
D. `3(1)/(6)`

Answer

To solve the problem, we start with the given equation:

\[ \frac{a}{8} = \frac{b}{9} = \frac{c}{6} = k \]

where \( k \) is a common ratio. This allows us to express \( a \), \( b \), and \( c \) in terms of \( k \):

1. **Express \( a \), \( b \), and \( c \) in terms of \( k \)**:
- From \( \frac{a}{8} = k \), we have:
\[ a = 8k \]
- From \( \frac{b}{9} = k \), we have:
\[ b = 9k \]
- From \( \frac{c}{6} = k \), we have:
\[ c = 6k \]

2. **Substitute \( a \), \( b \), and \( c \) into the expression \( \frac{a + b + c}{c} \)**:
\[ a + b + c = 8k + 9k + 6k = 23k \]
Therefore, we can write:
\[ \frac{a + b + c}{c} = \frac{23k}{6k} \]

3. **Simplify the expression**:
\[ \frac{23k}{6k} = \frac{23}{6} \]

4. **Final answer**:
The value of \( \frac{a + b + c}{c} \) is:
\[ \frac{23}{6} \]

5. **Convert to mixed fraction**:
\[ \frac{23}{6} = 3 \frac{5}{6} \]

Thus, the final answer is \( 3 \frac{5}{6} \).